Beam search decoding. RealiT implements this search strategy via a beam search decoding [1]}. Here, we iterate the top-\(k\)  bug locations according to the model and for each bug location we again search for the top-\(k\)  token repairs. During this process, we only store pairs that are assigned the highest likelihood together. Afterwards, we filter the candidate pairs to only meaningful repairs: If the model predicts a bug location then this should be fixed by a different token of the same type. Combinations of the special NOOP location and repair are always meaningful (since nothing will be changed).
Finally, as a result, RealiT computes the most likely meaningful repair operation:
\(\text{replace} (t_{l^\prime }, r^\prime ) \text{ with } \langle l^\prime , r^\prime \rangle = \text{argmax } p ( \langle l, r \rangle \mid \mathcal {T})\) 
